Blender equivalent of 'graph materials on selected objects'?
Dragging image in scene is equivalent of Add > Image > Reference, creates help Empty object. It's a relatively new feature since 2.80 and there is no native way to convert it to mesh object.

You need to enable addon Import Images as Planes and then you will have Image > Images as Planes operator in Add menu, witch create plane with proportions of image and do the shader node setup including transparency.